Complexification of Gauge Theories

For the case of a first-class constrained system with an equivariant momentum map, we study the conditions under which the double process of reducing to the constraint surface and dividing out by the group of gauge transformations $G$ is equivalent to the single process of dividing out the initial phase space by the complexification $G_C$ of $G$. For the particular case of a phase space action that is the lift of a configuration space action, conditions are found under which, in finite dimensions, the physical phase space of a gauge system with first-class constraints is diffeomorphic to a manifold imbedded in the physical configuration space of the complexified gauge system. Similar conditions are shown to hold in the infinite-dimensional example of Yang-Mills theories. As a physical application we discuss the adequateness of using holomorphic Wilson loop variables as (generalized) global coordinates on the physical phase space of Yang-Mills theory.Comment: 25pp., LaTeX, Syracuse SU-GP-93/6-2, Lisbon DF/IST 6.9

Fish passage hydrodynamics New Zealand context

New Zealand is home to 57 native freshwater fish species, of which a considerable number are diadromous, having to move between freshwater and saltwater at least once during their lifecycle. The economic utilisation of New Zealand rivers has largely been carried out without fish migration behaviour in mind, resulting in thousands of structures that prevent fish migration up- and downriver. Remediation of existing structures, especially culverts, and construction of new, more fish friendly, structures requires in-depth knowledge of the needs of the target fish species. In April 2018, the New Zealand Fish Passage Guidelines were released, providing a design framework to enable fish passage in new and existing structures. In support of the new guidance, our project aims to gain insight into the swimming behaviour and performance of inanga (Galaxias maculatus) under various hydraulic conditions, in particular when swimming upstream, which is not well understood. For this purpose, we are designing a new experimental setup in a 600 mm wide flume at the Water Engineering Laboratory at the University of Auckland. We will study hydrodynamics of fish passes with roughened surfaces, baffles and energy dissipators. We will evaluate sensor equipment used to enable flow and fish tracking, with the intention of tracking individual inanga at critical cross sections. This will allow us to study fish response to turbulence, boundary layers, resting zones and wetted margins. We aim to gain valuable insight into design methods and materials that best help inanga, and potentially other members of the family Galaxiidae, with their migration. Eventually, the project aims to provide guidelines suitable for retrofitting existing and building new structures

The High Magnetic Field Phase Diagram of a Quasi-One Dimensional Metal

We present a unique high magnetic field phase of the quasi-one dimensional organic conductor (TMTSF)$_2$ClO$_4$. This phase, termed "Q-ClO$_4$", is obtained by rapid thermal quenching to avoid ordering of the ClO$_4$ anion. The magnetic field dependent phase of Q-ClO$_4$ is distinctly different from that in the extensively studied annealed material. Q-ClO$_4$ exhibits a spin density wave (SDW) transition at $\approx$ 5 K which is strongly magnetic field dependent. This dependence is well described by the theoretical treatment of Bjelis and Maki. We show that Q-ClO$_4$ provides a new B-T phase diagram in the hierarchy of low-dimensional organic metals (one-dimensional towards two-dimensional), and describe the temperature dependence of the of the quantum oscillations observed in the SDW phase.Comment: 10 pages, 4 figures, preprin

On two superintegrable nonlinear oscillators in N dimensions

We consider the classical superintegrable Hamiltonian system given by $H=T+U={p^2}/{2(1+\lambda q^2)}+{{\omega}^2 q^2}/{2(1+\lambda q^2)}$, where U is known to be the "intrinsic" oscillator potential on the Darboux spaces of nonconstant curvature determined by the kinetic energy term T and parametrized by {\lambda}. We show that H is Stackel equivalent to the free Euclidean motion, a fact that directly provides a curved Fradkin tensor of constants of motion for H. Furthermore, we analyze in terms of {\lambda} the three different underlying manifolds whose geodesic motion is provided by T. As a consequence, we find that H comprises three different nonlinear physical models that, by constructing their radial effective potentials, are shown to be two different nonlinear oscillators and an infinite barrier potential. The quantization of these two oscillators and its connection with spherical confinement models is briefly discussed.Comment: 11 pages; based on the contribution to the Manolo Gadella Fest-60 years-in-pucelandia, "Recent advances in time-asymmetric quantum mechanics, quantization and related topics" hold in Valladolid (Spain), 14-16th july 201

Clinical and laboratory variability in a cohort of patients diagnosed with type 1 VWD in the United States

Von Willebrand disease (VWD) is the most common inherited bleeding disorder, and type 1 VWD is the most common VWD variant. Despite its frequency, diagnosis of type 1 VWD remains the subject of much debate. In order to study the spectrum of type 1 VWD in the United States, the Zimmerman Program enrolled 482 subjects with a previous diagnosis of type 1 VWD without stringent laboratory diagnostic criteria. VWF laboratory testing and full length VWF gene sequencing were performed for all index cases and healthy control subjects in a central laboratory. Bleeding phenotype was characterized using the ISTH Bleeding Assessment Tool. At study entry, 64% of subjects had VWF:Ag or VWF:RCo below the lower limit of normal, while 36% had normal VWF levels. VWF sequence variations were most frequent in subjects with VWF:Ag < 30 IU/dL (82%) while subjects with type 1 VWD and VWF:Ag ≥ 30 IU/dL had an intermediate frequency of variants (44%). Subjects whose VWF testing was normal at study entry had a similar rate of sequence variations as the healthy controls at 14% of subjects. All subjects with severe type 1 VWD and VWF:Ag ≤ 5 IU/dL had an abnormal bleeding score, but otherwise bleeding score did not correlate with VWF:Ag level. Subjects with a historical diagnosis of type 1 VWD had similar rates of abnormal bleeding scores compared to subjects with low VWF levels at study entry. Type 1 VWD in the United States is highly variable, and bleeding symptoms are frequent in this population

Geometric Approach to Pontryagin's Maximum Principle

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

Mitotic phosphorylation by NEK6 and NEK7 reduces microtubule affinity of EML4 to promote chromosome congression

EML4 is a microtubule-associated protein that promotes microtubule stability. We investigated its regulation across the cell cycle and found that EML4 was distributed as punctate foci along the microtubule lattice in interphase but exhibited reduced association with spindle microtubules in mitosis. Microtubule sedimentation and cryo-electron microscopy with 3D reconstruction revealed that the basic N-terminal domain of EML4 mediated its binding to the acidic C-terminal tails of α- and β-tubulin on the microtubule surface. The mitotic kinases NEK6 and NEK7 phosphorylated the EML4 N-terminal domain at Ser144 and Ser146 in vitro, and depletion of these kinases in cells led to increased EML4 binding to microtubules in mitosis. An S144A-S146A double mutant not only bound inappropriately to mitotic microtubules but also increased their stability and interfered with chromosome congression. Meanwhile, constitutive activation of NEK6 or NEK7 reduced EML4 association with interphase microtubules. Together, these data support a model in which NEK6- and NEK7- dependent phosphorylation promotes dissociation of EML4 from microtubules in mitosis in a manner that is required for efficient chromosome congression

Cofactorization on Graphics Processing Units

We show how the cofactorization step, a compute-intensive part of the relation collection phase of the number field sieve (NFS), can be farmed out to a graphics processing unit. Our implementation on a GTX 580 GPU, which is integrated with a state-of-the-art NFS implementation, can serve as a cryptanalytic co-processor for several Intel i7-3770K quad-core CPUs simultaneously. This allows those processors to focus on the memory-intensive sieving and results in more useful NFS-relations found in less time

On the Use of the Negation Map in the Pollard Rho Method

The negation map can be used to speed up the Pollard rho method to compute discrete logarithms in groups of elliptic curves over finite fields. It is well known that the random walks used by Pollard rho when combined with the negation map get trapped in fruitless cycles. We show that previously published approaches to deal with this problem are plagued by recurring cycles, and we propose effective alternative countermeasures. As a result, fruitless cycles can be resolved, but the best speedup we managed to achieve is by a factor of only 1.29. Although this is less than the speedup factor of root 2 generally reported in the literature, it is supported by practical evidence